"I do not have a ticket."
”きっぷがありません” ⇒ There is no ticket. ”きっぷをもっていません” ⇒ I don't have a ticket. The meaning is slightly different. I think your translation is more natural Japanese.
If you forgot to bring a ticket, you say "I do not have a ticket." Maybe say this in Japanese ”きっぷがない” ”きっぷない”
”きっぷがありません”It ’s too calm and it ’s an interesting expression.
There's at least 10 fairly standard ways this could be expressed in Japanese and duo only seems accept the given answer. See https://context.reverso.net/translation/english-japanese/don't+have+a+ticket for two.
There are currently 104 possible answers that are accepted for this sentence, so we definitely accept more than one answer.
If you're talking about a listening exercise, then yes, only one possible answer is accepted. This is due to a limitation of Duolingo's programming, as we currently can't key in more than one acceptable answer for listening exercises.